$A$ plane passes through $(2,1,2)$ and $(1,2,1)$ and is parallel to the line $2x = 3y$ and $z = 1$. Then the plane also passes through which of the following points?

The direction cosines of a normal to the plane passing through $(4,2,3)$,$(-1,4,2)$ and $(3,2,1)$ are .....

The perpendicular distance of the origin from the plane $x-3y+4z-6=0$ is

$A$ plane meets the coordinate axes at $A, B, C$ such that the centroid of the $\Delta ABC$ is the point $(\alpha, \beta, \gamma)$. Show that the equation of the plane is $\frac{x}{\alpha} + \frac{y}{\beta} + \frac{z}{\gamma} = 3$.

Find the vector equation of the plane passing through the points $\hat{i} + \hat{j} - 2\hat{k}$,$2\hat{i} - \hat{j} + \hat{k}$,and $\hat{i} + 2\hat{j} + \hat{k}$.

If the foot of the perpendicular from $(0,0,0)$ to the plane is $(1,2,2)$, then the equation of the plane is